Discussion on a popular internet paradox

I treat this as a problem in logic or linguistics rather than statistics.


Key Questions: define what constitutes the option and define for each choice, what they signify. I propose three answers with their own logic here.
Ref: 1. http://en.wikipedia.org/wiki/Pragmatics
2. http://en.wikipedia.org/wiki/Semantics
3. http://en.wikipedia.org/wiki/Correspondence_theory_of_truth


I. Correspondence theory: 1/3
[The correspondence theory of truth states that the truth or falsity of a statement is determined only by how it relates to the world] (quote from wiki)
So there are only 3 choices to be exact. Because (A) and (D) merely signify the only corresponding fact of 25%. This matter-of-fact type of understanding will lead to probability of 1/3 as in Mayur’s answer. This also implies, we know the answer to the question is 25%. But the known fact is independent from answer to this question.

II. Semantico-referential meaning: (B) 50%
[Semantico-referential meaning… describes events in the world that are independent of the circumstance they are uttered in.] (excerption from wiki)
So there are 4 choices if we treat the signifiers as independent from their context. (A) and (D) both correspond to 25% but are independent (ignorant of where they appear). Then the answer will be (B) 50%. And when we answer to this question with (B), because we assumed independence from context, we do not alter the probability.

III. Pure indexical sign: (A) or (D) 25%
[A pure indexical sign does not contribute to the meaning of the propositions at all.] (quote from wiki)
If we understand the choices as purely indexical, then the answer is (A) or (D) 25%. And because sentences are themselves also purely indexical, so it does not affect the meaning or the proposition itself.

IV. Others: 0%
Another popular answer to this question is 0%. I have yet to define the logic behind this answer and have no intention of future attempt. But I generally agree to the fact that if Choice (C) 60% is replaced by 0%, this paradox becomes even better.